It's the superlative form of the adjective "ο αναιδής" ; here are the 3 degrees of the adjective: ο αναιδής-ο αναιδέστερος-ο αναιδέστατος. Its meanings in English according to this online dictionary: impudent, impertinent, shameless, brazen, brassy, brash, insolent, rude.
"Αναιδής" is formed by the prefix "αν-",which indicates the negation, and "αιδώς", which means "respect/reverence".

I'll have to add, that with the passing of time that word has taken up a life of its own so to speak.
Almost like it is a full-blown adjective (meaning very rude, very impudent, very impolite) and not the superlative of another adjective...

I'll have to add, that with the passing of time that word has taken up a life of its own so to speak.
Almost like it is a full-blown adjective (meaning very rude, very impudent, very impolite) and not the superlative of another adjective...

Click to expand...

That's correct, which also applies to many other superlative forms of adjectives (άριστος, μέγιστος, ελάχιστος, κάκιστος etc) or adverbs ( άριστα, ελάχιστα, μάλιστα etc. ).
I mostly highlighted the grammar of the word, which might be unnecessary, and less its role.